Simulink Control Design™ - MathWorks

Name: C2

Continuous-time PI controller in parallel form.

Next use "LoopShape" requirements to specify the desired bandwidths for the inner and

outer loops. Use as the target loop shape for the outer loop to enforce integral

action with a gain crossover frequency at 0.2 rad/s:

% Outer loop bandwidth = 0.2

s = tf('s');

Req1 = TuningGoal.LoopShape('y1',0.2/s); % loop transfer measured at y1

Req1.Name = 'Outer Loop';

Use for the inner loop to make it ten times faster (higher bandwidth) than the outer

loop. To constrain the inner loop transfer, make sure to open the outer loop by specifying

y1 as a loop opening:

% Inner loop bandwidth = 2

Req2 = TuningGoal.LoopShape('y2',2/s); % loop transfer measured at y2

Req2.Openings = 'y1'; % with outer loop opened at y1

Req2.Name = 'Inner Loop';

You can now tune the PID gains in C1 and C2 with systune:

ST = systune(ST0,[Req1,Req2]);

Final: Soft = 0.859, Hard = -Inf, Iterations = 70

Use showTunable to see the tuned PID gains.

showTunable(ST)

Block 1: rct_cascade/C1 =

1 s

Kp + Ki * --- + Kd * --------

s Tf*s+1

with Kp = 0.0501, Ki = 0.0186, Kd = 0.0432, Tf = 0.00323

Name: C1

Continuous-time PIDF controller in parallel form.

13 Control System Tuning Examples